Sampling Reese's Pieces Activity

Sampling Reese’s Pieces – Student Handout
This activity is based on an adaptation by Joan Garfield and Dani Ben-Zvi of an activity from Rossman and
Chance (2000), Workshop Statistics: Discovery with Data, 2nd Edition.
1. Reese’s Pieces candies have three colors: orange, brown, and yellow. Which color
do you think has more candies in a package: orange, brown or yellow?
2. Guess the proportion of each color in a bag:
Orange____
Brown____ Yellow______
3. If each student in the class takes a sample of 25 Reese’s pieces, would you expect
every student to have the same number of orange candies in their sample?
Explain.
4. Pretend that 10 students each took samples of 25 Reese’s pieces. Write down the
number of orange candies you might expect for these 10 samples:
___ ___ ___ ___ ___ ___ ___ ___ ___ ___
These numbers represent the variability you would expect to see in the number of
orange candies in 10 samples of 25 pieces.
You will be given a cup that is a random sample of Reese’s pieces. Count out 25
candies from this cup without paying attention to color. In fact, try to IGNORE the
colors as you do this.
5. Now, count the colors for your sample and fill in the chart below:
Orange Yellow Brown
Number of candies _____ _____ _____
Proportion of candies _____ _____ _____
(divide each NUMBER
by 25)
Write the number AND the proportion of orange candies in your sample on the board.
Mark where each value should be on the two dotplots your teacher constructs (one for
number of oranges, one for proportion of oranges).
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I. Discussion: The proportions are the sample statistics. For example, the proportion of
orange candies in your sample is the statistic that summarizes your sample.
How does this relate to the population parameter (the proportion of all orange
Reese’s Pieces produced by Hershey Co.)?
Do you know the value of the parameter?
Do you know the values of the statistics?
Does the value of the parameter change, each time you take a sample?
Does the value of the statistic change each time you take a sample?
Did everyone in the class have the same number of orange candies?
How do the actual sample values compare to the ones you estimated earlier?
Did everyone have the same proportion of orange?
Describe the variability of the distribution of sample proportions on the board
in terms of shape, center, and spread.
II. Focus on the proportion of orange candies.
Simulate data and tie this activity to the Three-Tier Simulation Process Model (SPM).
Use the SPM to fill in information for the three tiers:
Population:
Samples and sample statistics:
Distribution of sample statistics:
Fill in the details of the distribution that was put of the board in the SPM below:
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Based on the distribution we obtained (on the board), what would you ESTIMATE to
be the population parameter, the proportion of orange Reese’s pieces produced by
Hershey?
What if everyone in the class only took 10 candies, in their sample instead of 25? Do
you think the graphs on the board would look the same? If not, how would they be
different?
What if everyone in the class took 100 candies? Would the distributions on the board
change at all? If so, how?
III. The Reese’s Pieces Applet
Instead of trying this activity again with fewer or more candies, simulate the activity
using a web applet. Go to www.rossmanchance.com/applets/, and look at the bottom
of the far right column to find Java Applets. Click on Java Applets and look for
Sampling Distributions, and click on Reese’s Pieces. You will see a big container of
colored candies: that represents the POPULATION.
How many orange candies are in the population?
You will see that the proportion of orange is already set at .45, so that is the
population parameter. (People who have counted lots of Reese’s pieces came up
with this number).
How does .45 compare to the proportion of orange candies in your sample?
How does it compare to the center of the class’ distribution?
Click on the “draw samples” button. One sample of 25 candies will be taken and the
proportion of means for this sample is plotted on the graph. Repeat this again.
Do you get the same or different values for each sample?
How do these numbers compare to the ones our class obtained?
How close is each sample statistic (proportion) to the POPULATION
PARAMETER?
Turn off the animation and change the number of samples to 100.
Click on draw samples, and see the distribution of sample statistics built.
Describe its shape, center and spread.
How does this compare to the one our class constructed on the board?
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IV. Test your conjectures
What happens to this distribution of sample statistics as we change the number of
candies in each sample (sample size).
First, change the sample size to 10 and draw 100 samples
.
How close is each sample statistic (proportion) to the POPULATION
PARAMETER?
Next, change the sample size to 100 and draw 100 samples.
V. Sample Size
How close is each sample statistic (proportion) to the POPULATION
PARAMETER?
As the sample size increases, what happens to how well the sample statistics resemble
the population parameter?
Now, describe the effect of sample size on the distributions of sample statistics.
Note: When we generate sample statistics and graph them we are generating an
estimated SAMPLING DISTRIBUTION, or a distribution of the sample
statistics. It looks like other distributions we have seen of raw data. What’s
different about this?
We now need to distinguish between THREE kinds of distributions of data:
Distribution of population
Distribution of one sample of data
Distribution of sample statistics for many samples.
Show where each of the distributions are represented on the SIMULATION PROCESS
MODEL. Be sure to turn this in before you leave class today.
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